99-10   Berichtsreihe des Mathematischen Seminars der Universität Kiel

Detlef Bargmann, Walter Bergweiler:

Periodic points and normal families

Let F be the family of all functions which are holomorphic in some domain and do not have periodic points of some period greater than one there. It is shown that F is quasinormal, and the sequences in F which do not have convergent subsequences are characterized. The method also yields a new proof of the result that transcendental entire functions have infinitely many periodic points of all periods greater than one.

Mathematics Subject Classification (1991): 30D05, 30D45, 58F23

Bibliographical note: Proc. Amer. Math. Soc. 129, 2881-2888 (2001)

Mail an Jens Burmeister
[Thu Feb 19 18:56:34 2009]